Impossible to centrifuge salt out of water?

I've been told (by my highschool chemistry teacher, which obviously means it isn't necessarily true), that when salt dissolves in water, that you cannot centrifuge it out.

I understand that you can't centrifuge it out like you would sugar, or something that doesn't ionize, but it seems to me that you should be able to centrifuge it out.

Water can only accept a concentration of so many salt ions per so many water molecules, and once that acceptable concentration is exceeded, salt will precipitate out of solution, correct?

Furthermore, when salts dissolve in water, and the ions dissociate, the positive ions will tend to stick near the - end of water, and the negative ions will be attracted to the positive end of water. So, if you're dealing with an unsaturated solution, you have some water molecules that essentially have ions loosely bonded to them, making them heavier.

In that the water molecules that have ions attracted to them are heavier, it seems that if you centrifuge water, these molecules will go to the bottom of the centrifuge tube.

If you were to use enough force, it should seem that you'd get enough of the water with ions attracted to it to go to the bottom that you might actually surpass the molarity of ions that water can take, and that some salt would actually previpitate out.

Even if you couldn't get the proper ratio of ions to water molecules for salt to precipitate out, it seems that the ionic sides of the water should be sent furthest down, since the ions of any salt are heavier than water's components.